We describe the structure and use of epidemiology models of disease transmission, with an emphasis on the susceptible/infected/recovered (SIR) model. We discuss high-profile forecasts of cases and deaths that have been based on these models, what went wrong with the early forecasts, and how they have adapted to the current COVID pandemic. We also offer three distinct areas where economists would be well positioned to contribute to or inform this epidemiology literature: modeling heterogeneity of susceptible populations in various dimensions, accommodating endogeneity of the parameters governing disease spread, and helping to understand the importance of political economy issues in disease suppression.